Why are all my edges darker when using texture paint
Since it goes away with a subsurf it is a problem with too little geometry - too few edge loops to get a good interpolation across the edge. 
You can 


Use manual loops along the discs
Use edge split modifier to not interpolate across the sharp edges
Use the Bevel Modifier (if it doesn't work, google how to use it, or
send me a screenshot of your settings)


EIDT: I just realized, the subsurf modifier you mentioned might also mess with your UVs, try toggling split UVs in the settings.